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We present new solution of the the connection problem for local solutions tothe general Heun equation. Our approach is based on the symmetric form of theHeun's differential equation \cite{Fiziev14,Fiziev16} with four differentregular singular points $z_{1,2,3,4}$. The four special regular points in thecomplex plane: $Z_{123},Z_{234},Z_{341},Z_{412}$ are the centers of thecircles, defined by the different triplets $\{z_k,z_l,z_m\}$ with correspondingdifferent indexes and play fundamental role, since the coefficients of theconnection matrix can be expressed using the values of local solutions of thegeneral Heun's equation at these points. A special case when all coefficientscan be calculated using only one of the points $Z_{klm}$ is also considered.

A new approach to the connection problem for local solutions to the general Heun equation